Answered

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A ball of mass M and speed of V collides head on with a ball of mass 2M and a speed of v/2, as
shown above. If the two balls stick together, their speed after the collision is

Sagot :

VirαtKσhli

Answer:

2/3V

Explanation:

Given that a ball of mass M and speed V collides with another ball of mass 2M and velocity v/2 . After collision they stick together and we need to find their speed after collision . According to Law of Conservation of Momentum , The total momentum of the system before and after collision is constant .That is ;

[tex]\sf\qquad\longrightarrow m_1u_1+m_2u_2=m_1v_1+m_2v_2\\ [/tex]

[tex]\sf\qquad\longrightarrow MV + 2M\bigg(\dfrac{V}{2}\bigg) = (2M + M)(v)\\ [/tex]

[tex]\sf\qquad\longrightarrow MV +MV= 3Mv\\[/tex]

[tex]\sf\qquad\longrightarrow 2MV = 3Mv\\ [/tex]

[tex]\sf\qquad\longrightarrow v =\dfrac{2M}{3M}V\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{ v_{after\ collision}=\dfrac{2}{3}V }[/tex]

Hence the velocity after the collision ia 2/3V .

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